Study On Signal Reconstruction Algorithms For Compressed Sensing

Compressed sensing (CS) is a new sampling theory with a rapid development in recentyears, and it provides a method to recover the original signal from a small amount ofsamples. CS makes the signal compression during the sampling for the sparse andcompressible signal, thus, makes the compressible progress and the sampling process intoone. CS breaks the shackles of Nyquist law and saves a lot of storage, transmission, andcomputing resources. CS demonstrates outstanding advantages and a broad applicationprospects in the field of modern signal processing.Firstly, this paper presents an overview of the theoretical framework of CS. It includesthree parts: sparse representation of the signal, the design of measurement matrix, andreconstruction of the signal. This thesis describes the history of the decomposition for thesparse signal and makes a in-depth research for measurement matrix.For the part of signal reconstruction, the principle of some common reconstructionalgorithm has been presented. Secondly, this paper focus on the basis pursuit algorithm (BP)and basis pursuit do-nosing algorithm and compares the improved algorithm with theoriginal algorithm through simulation and verification. The results show that the proposedalgorithm could effectively improve the reconstruction accuracy of the signal and BPalgorithm could be used to the signal which contains impulse noise through theimprovement to the algorithm, which extends the scope of its application. Finally, thispaper briefly summarizes the classification of greedy algorithms and compared their timecomplexity and reconstruction accuracy between the matching pursuit algorithm andorthogonal matching pursuit algorithm.